Question 884000
p = 2/3 = proportion of doctors claimed to be recommending a particular pain killer.
q = 1 - p = 1/3 = proportion of doctors not claimed to be recommending a particular pain killer.
n = 300 = number of doctors in the sample.


population mean is assumed to be n * p = 300 * 2/3 = 200.


the population standard deviation is assumed to be sqrt (p * q * n) which is equal to sqrt (300  * 2/3 * 1/3) = sqrt(600/9).


z score is equal to (180 - 200) / sqrt(600/9) which is equal to -2.45.


look up in z score table for z score of -2.45 and you'll find that the area to the left of that z score is equal to .0071.


the probability that someone will have a score less than 180 is equal to .0071.


z score table used can be found <a href = "http://lilt.ilstu.edu/dasacke/eco148/ztable.htm" target = "_blank">HERE</a>